Let's break down the problem presented in the image to understand where the calculation may have gone wrong for the new median.

Given:

• The mean salary of 5 employees is $41,900.
• There are two modes for the salaries: $34,500 and $50,000.
• The median salary receives a raise of $2,700.

Part a: New Mean

We know that the total sum of all salaries is calculated by multiplying the mean salary by the number of employees: $\text{Total Sum} = \text{Mean} \times \text{Number of Employees} = 41,900 \times 5 = 209,500$ If the median salary gets a raise of $2,700, the total sum will increase by $2,700. The new total sum is: $\text{New Total Sum} = 209,500 + 2,700 = 212,200$ Now, the new mean is the new total sum divided by the number of employees: $\text{New Mean} = \frac{212,200}{5} = 42,440$ This confirms the correct value given in part (a).

Part b: New Median

To correctly calculate the new median, we need to determine the initial median before the raise and adjust accordingly.

Since there are 5 employees, the median is the 3rd salary when arranged in order. The modes suggest that some employees earn $34,500 and others $50,000, but we aren't explicitly told the exact distribution of the other salaries. However, let's assume the original median was a salary between those modes, likely $41,900 (the original mean).

When the median salary gets a $2,700 raise, the new median becomes: $\text{New Median} = 41,900 + 2,700 = 44,600$

So, the correct new median should be $44,600, not $93,200 as indicated in the image.

Would you like further details on this process or help with any other calculations?

Here are 5 follow-up questions for deeper understanding:

1. How do you determine the median in a dataset with an even number of values?
2. What happens to the mean if one salary is drastically different from the others?
3. Can there be more than one median in a dataset? Why or why not?
4. How would the mean change if a salary below the current median received the raise instead?
5. What effect do raises or decreases in the highest or lowest salaries have on the mean?

Tip: The median is less sensitive to outliers than the mean, which makes it a better measure of central tendency when dealing with extreme values.